# RMS speed in kinetic energy equation for gas

• I
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## Main Question or Discussion Point

I have been pondering. Why is it that we use the rms speed in the equation Ek = 1/2 m vrms2, as opposed to just the mean speed2

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mjc123
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Because kinetic energy is 1/2 mv2. The kinetic energy of molecule i is 1/2 mvi2, so the average kinetic energy is 1/2m * (average of v2). If you used the square of the mean speed you would get a different, wrong answer. (The mean velocity is, of course, zero.)

Because kinetic energy is 1/2 mv2. The kinetic energy of molecule i is 1/2 mvi2, so the average kinetic energy is 1/2m * (average of v2). If you used the square of the mean speed you would get a different, wrong answer. (The mean velocity is, of course, zero.)
I agree

Gold Member
Thanks for your help with that mjc 123 and lychette, it makes much more sense now.

We are using V(rms) as mean velocity of the system will come out to be zero as particles are moving randomly in all the directions, So Rms (Root Mean Square) is taken.

V^2(Rms) = N1 x V1^2 + N2 x V2^2 Divided by N1 + N2

Here N is molecule and V is its velocity. As it is a square all velocities will become positive.

mjc123